Book cover for Algebra A Combined Function

Algebra A Combined Function

Elayn Martin-Gay

ISBN #9780321726391

4th Edition

6,670 Questions

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28,872 Students Helped

Homework Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This section focuses on reading and analyzing data from bar and line graphs, as well as plotting and interpreting ordered pairs on the rectangular coordinate system. Key techniques include comparing bar lengths, reading numerical scales, and understanding how to locate points using coordinates. These skills are essential for making data-driven decisions and drawing meaningful conclusions from various types of graphs.

Learning Objectives

1

Interpret bar graphs and line graphs to extract quantitative information.

2

Describe and plot ordered pairs on the rectangular coordinate system.

3

Analyze relationships between paired data and determine missing coordinates.

4

Apply graph-reading techniques to real-world data examples.

Key Concepts

CONCEPT

DEFINITION

Bar Graph

A graph that uses bars to compare quantities across different categories. The length of each bar represents the value for that category.

Line Graph

A graph that uses points connected by lines to show trends or relationships over time, depicting how one variable changes with respect to another.

Ordered Pair

A pair of numbers (a, b) used to represent a point on the coordinate plane, where 'a' is the x-coordinate and 'b' is the y-coordinate.

Rectangular Coordinate System

A two-dimensional system defined by two perpendicular number lines (axes), the x-axis (horizontal) and y-axis (vertical), that intersect at the origin.

Origin

The intersection of the x-axis and y-axis at the point (0, 0) in the coordinate plane.

Quadrants

The four regions of the coordinate plane divided by the x-axis and y-axis, usually labeled with Roman numerals I, II, III, and IV.

Example Problems

Example 1

The following bar graph shows the top 10 tourist destinations and the number of tourists that visit each country per year. Use this graph to answer Exercises 1 through 6. See Example 1. Which country shown is the most popular tourist destination?

Example 2

The following bar graph shows the top 10 tourist destinations and the number of tourists that visit each country per year. Use this graph to answer Exercises 1 through 6. See Example 1. Which country shown is the least popular tourist destination?

Example 3

The following bar graph shows the top 10 tourist destinations and the number of tourists that visit each country per year. Use this graph to answer Exercises 1 through 6. See Example 1. Which countries shown have more than 40 million tourists per year?

Example 4

The following bar graph shows the top 10 tourist destinations and the number of tourists that visit each country per year. Use this graph to answer Exercises 1 through 6. See Example 1. Which countries shown have fewer than 30 million tourists per year?

Example 5

The following bar graph shows the top 10 tourist destinations and the number of tourists that visit each country per year. Use this graph to answer Exercises 1 through 6. See Example 1. Estimate the number of tourists per year whose destination is Italy.
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Step-by-Step Explanations

QUESTION

How do you determine the region with the most Internet users from a bar graph?

STEP-BY-STEP ANSWER:

Step 1: Observe the graph to identify all the bars representing different regions.
Step 2: Compare the lengths of the bars; the longest bar indicates the region with the highest value.
Step 3: Trace from the end of the longest bar horizontally to the numerical scale to approximate the total number of users.
Final Answer: The region with the most Internet users is the one with the longest bar (e.g., Asia/Oceania/Australia with approximately 785 million users, in Example 1).

Bar Graph Interpretation

QUESTION

How do you plot the ordered pair (3, 2) on the rectangular coordinate system?

STEP-BY-STEP ANSWER:

Step 1: Begin at the origin (0, 0).
Step 2: Move 3 units to the right along the x-axis because the first coordinate is 3 (positive).
Step 3: From that position, move up 2 units along the y-axis since the second coordinate is 2 (positive).
Final Answer: The point (3, 2) is plotted 3 units right and 2 units up from the origin.

Plotting an Ordered Pair

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Common Mistakes

  • Misreading the scale on the numerical axis, leading to incorrect approximations of values.
  • Confusing the order of coordinates when plotting points (e.g., switching x and y values).
  • Failing to correctly interpret steep changes in line graphs, which can obscure the moment of greatest change.
  • Not recognizing that the axes themselves do not belong to any quadrant, thus misidentifying the location of points.